Nasa Hataoka (photo below) matched Law at 13-under 200 at breezy Kingsmill Resort, rebounding from a bogey on the par-4 14th with an eagle on the par-5 15th in a 65.
"I wasn't thinking about where I was going to get a bogey or anything like that, so when it came, it came," Hataoka said. "Then I just cleared it."
The Japanese player won the Kia Classic in Carlsbad, California, in late March for her third LPGA Tour title.
Law is winless on the tour. The Englishwoman starred at UCLA.
"Obviously, winning is everything, right?" Law said "That's why we play this game. I'm going to do my very best to go out and get the win."
American Jennifer Song, tied for the lead after each of the first two rounds, had a 68 to fall a shot back along with Brooke Henderson. Song, the former University of Southern California player, also is winless on tour.
"The toughest part about today was the wind was just switching here and there," Song said. "It was kind of hard to make decisions with my club."
Henderson had a 64.
"This year, it's a little bit windier too than it has been in the past and you're getting a lot of roll around the tee and on the greens, too," the Canadian said. "You just have to play smart around this golf course."
Carlota Ciganda was 11 under after a 68, and Madelene Sagstrom had a 69 to get to 10 under.
The U.S. Women's Open is next week at the Country Club of Charleston in South Carolina.